Download Resistance

Physics 272
February 10
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
[email protected]
PHYS272 - Spring 15 - von Doetinchem - 240
Current, drift velocity, current density
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Amount of charge flowing through an area:
Current in a conductor is the product of the density of moving
charged particles, the magnitude of charge of each such
particle, the magnitude of the drift velocity, and the crosssection area
PHYS272 - Spring 15 - von Doetinchem - 241
Resistivity
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Generally current density in
conductor depends on electric field
and the properties of the material as
a function of temperature
Ohm's law:
Source: http://de.wikipedia.org/wiki/Georg_Simon_Ohm
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Resistivity  of a material is the ratio of electric field and
current density → do not confuse with resistance!
The greater the resistivity the greater the field has to be
to achieve the same current density
PHYS272 - Spring 15 - von Doetinchem - 242
Resistivity
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Perfect conductors would have zero resistivity
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Perfect insulators have an infinite resistivity
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Metals have a ~1022 times smaller resistivity than
insulators
Inverse of the resistivity is the conductivity
Ohm's law is not perfect and can only be applied for
certain temperature ranges
A conductor is called ohmic or linear if the resistivity
in a certain temperature range does not depend on
the value of the electric field
PHYS272 - Spring 15 - von Doetinchem - 243
Resistivity and temperature
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Resistivity in a metal nearly always increases with
temperature due to more vibration of the ions in the material
Behavior over a small temperature range can be described by:
Measuring the resistivity is a sensitive measure of
temperature, e.g., thermistor use semiconductor materials
Superconductivity: sudden change to zero resistivity at cold
temperatures of certain materials: electrons flow freely without
creating heat in the conductor
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Quench of superconducting magnets at CERN
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Resistance
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Current and potential difference are easier to
measure than current density and electric field
As current flow through electric potential difference
→ electric potential energy is lost
→ energy goes into the ions
PHYS272 - Spring 15 - von Doetinchem - 246
Interpreting resistance
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Resistance is proportional to length and inversely proportional to
cross-section
Analogy:
–
a narrow hose has more
resistance than a wide one
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a long hose has a larger
resistance than a short
one
Circuit device with a
certain resistance is
called a resistor
Common values:
–
1-1,000,000Ohm
Source: http://en.wikipedia.org/wiki/Resistor
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Resistance
https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html
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Resistance
https://phet.colorado.edu/en/simulation/battery-resistor-circuit
PHYS272 - Spring 15 - von Doetinchem - 249
Electromotive force and circuits
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You need a complete circuit to have a steady
current
If a charge goes around a complete circuit it will
lose potential energy to the ions in the conductor
For a steady current a device that is pushing the
charge to a higher potential is needed:
source of electromotive force (emf)
Examples: batteries, generators, solar panels
transform, e.g., chemical, mechanical energy into
electric energy
Ideally: provide constant potential difference, not
depending on current
PHYS272 - Spring 15 - von Doetinchem - 252
Electromotive force and circuits
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Ideal source of emf
brings charge to higher
potential energy level
without increasing the
kinetic energy
Charge is not used up in
a circuit and is not
accumulating in the
circuit elements. Both
sides of the terminal of a
battery have the same
current for an ideal
source of emf.
low potential
high potential
Be careful of charge sign:
Electrons would like to go to b
(against the electric field)
→ have to be moved to a to
increase the potential energy
PHYS272 - Spring 15 - von Doetinchem - 253
Emf in animals: electric eel
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Rebuild muscles
produce electric
potential
differences that
are combined (in
series) to produce
strong shocks
(500V at ~0.8A)
cells pump positive
sodium and
potassium ions out
of the cell via
transport proteins
http://www.youtube.com/watch?v=1EEy-aXHzRI
PHYS272 - Spring 15 - von Doetinchem - 254
Internal resistance
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Charges move through the material of a real source of
emf feel an internal resistance
If the internal resistance behaves like ohmic resistance:
For a real source of emf, the terminal voltage equals the
emf only if no current is flowing through the source.
Current in a circuit drops if the external resistance is
getting bigger.
Car battery delivers less current when the internal
resistance is higher at colder temperatures
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Symbols for circuit diagrams
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Conductor with negligible
resistance
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Resistor
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Source of emf
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Source of emf with internal
resistance
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Voltmeter
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Ammeter
PHYS272 - Spring 15 - von Doetinchem - 258
Source in a complete circuit
No potential difference
between a-a' and b-b'
We define the direction
electric current as
going away from the
positive side of our
source of emf
(although electrons
move the other way
around)
Can be very dangerous
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Potential changes around a circuit
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Net change in potential energy for a charge in a
complete circuit must be zero
→ algebraic sum of potential differences around a
circuit must be 0
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Energy and power in electric circuits
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How fast is energy delivered or extracted?
If a charge passes through a circuit element: change of
potential energy
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Current stays the same → no gain of kinetic energy
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Power:
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Power for a pure resistance:
PHYS272 - Spring 15 - von Doetinchem - 261
Power
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Moving charges collide with atoms in resistor
→ increase internal energy of material (energy dissipation)
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Maximum power rating of resistors before it overheats
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Power output:
I2r
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Power input:
Direction does not
matter for a resistor →
energy is dissipated in
any case
Source with larger emf pushes current backward through source with lower emf
(charging of car battery with alternator)
PHYS272 - Spring 15 - von Doetinchem - 262
Power
2
2
I r=4A 2=8W
I2r
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Increasing external resistance reduces power input to
resistor
Shorted circuit (R=0):
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No net power output
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dissipates all energy within the source: quickly ruins battery
PHYS272 - Spring 15 - von Doetinchem - 263
Tolman-Stewart experiment
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How do we know that the free charges in a metal
are negative?
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Abruptly stop a rapidly spinning spool of wire and
measure the potential difference between the ends of the
wire
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Simplified version: accelerate a metal rod uniformly
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Charges lag behind rod motion → electric field builds up
PHYS272 - Spring 15 - von Doetinchem - 264
Tolman-Stewart experiment
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